Types of (Aristotelian) Enthymemes, and Proofs

An enthymeme is for Aristotle a technical proof, which differs the syllogism in the number of premises. The syllogism is exhaustive in its enumeration of premises, while the enthymeme is not. This is not due, according to Carlo Ginzburg, to a lack of logical rigor, but because of the rhetorical perspective were the enthymeme is immersed (Ginzburg, 41). Aristotle states that the enthymeme is fed by four sources: eikos (likelihood), paradeigma (example), semeion (signs), and tekmerion (necessary sign). These four terms are quiantifyers of the relationship between the sign and the signate, i.e. the thing or event signified. Which is the quantitative difference in the strength of conclusions afforded by these proofs?

These terms represent the intermediate marks in a probability scale that ranges from 1 (complete certainty) to zero (no certainty). So the weight (from 0 to 1) carried by enthymemes fed by proofs evinced by these terms is for Aristotle:

1 = tekmeria > semeion > eikos > 0

Graphically:

A conclusion arrived by by tekmerion proofs is beyond refutation. These kinds of proofs provide an "inevitable and necessary relationship between sign and signate" (Grimaldi).
Now, what's the difference in the strength of probability for semeion and eikos? "The relation of each (semeion vs eikos) to what they indicate as probable is different." (Grimaldi, 396). Semeion enthymemes will not carry a demonstrative weight as tekmeria will do; nevertheless, the probability afforded by semeia might still be high, as opposed to an eikos proof. "The semeion definitely and specifically points to the existence of the reality it argues to as probable"

With the eikos the reason to accept the probable fact which it seeks to establish is less obviously convincing. An eikos is a rough generalization, or what is called a moral universal, derived from experience, but related only in a general way to the particular instance it argues to as probable.

"In itself the semeion anonymon points to the specific signate with good probability. The eikos, even though eikos has its ground in the real order, carries in itself no formal relation as such to some specific fact. The eikos offers a measure of practical certainty about the probable conclusion it draws. The semeion, because of the natural relation between sign and signate in which the one implicates the presence of the other, offers a conclusion that is more secure and of higher probability." (Grimaldi, 397). "For example, it may or may not be true that the Olynthians have a fixed hatred for Philip as Demosthenes argues from the eikos [i.e. conjecturally] that those have an unshakeable hostility who hate another because of fear and of personal suffering. But [Demosthenes'] argument for Aeschines' hatred of himself is much more convincing, based, as it is, on Aeschines' harsh actions toward him, actions he calls semeia of personal animosity and jealousy". (Grimaldi, )

Ginzburg (p. 46) mentions other terms used to qualify the probatory strength of proofs used by other authors.

Xenophanes uses typoi, to mean traces of shells, fish, seals, etc. as evidence of an earlier stage in earth's history.

Thucydides uses tekmeria as evidence of phenomena that happened in Greece during the ancient past.